A197700 Decimal expansion of Pi/(1 + 2*Pi).

4, 3, 1, 3, 4, 8, 7, 1, 9, 1, 5, 0, 7, 9, 3, 5, 1, 4, 4, 2, 6, 7, 9, 3, 8, 3, 7, 1, 4, 5, 6, 7, 5, 3, 3, 2, 3, 9, 7, 9, 5, 3, 2, 3, 5, 5, 9, 7, 1, 7, 3, 1, 5, 2, 6, 0, 6, 3, 0, 8, 1, 4, 2, 0, 9, 9, 7, 6, 2, 9, 1, 1, 6, 7, 7, 7, 2, 3, 1, 0, 6, 0, 7, 3, 2, 2, 0, 7, 0, 7, 4, 0, 2, 1, 8, 5, 9, 4, 9

Offset

0,1

Comments

Least x > 0 such that sin(b*x) = cos(c*x) (and also sin(c*x) = cos(b*x)), where b=1/2 and c=Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Links

Table of n, a(n) for n=0..98.

Index entries for transcendental numbers

Example

0.4313487191507935144267938371456753323979...

Mathematica

b = 1/2; c = Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .43, .44}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197700 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 1}]
RealDigits[Pi/(1+2 Pi), 10, 120][[1]] (* Harvey P. Dale, Mar 31 2023 *)

Prog

(PARI) 1/(1/Pi+2) \\ Charles R Greathouse IV, Sep 30 2022

Crossrefs

Cf. A197682.

Sequence in context: A080758 A123683 A010306 * A006467 A119505 A201518

Adjacent sequences: A197697 A197698 A197699 * A197701 A197702 A197703

Keyword

nonn,cons

Author

Clark Kimberling, Oct 17 2011

Status

approved